I understand that 'the browser window does not seem like a limitation' as you stated. What's an app without one? Ok, let's not get metaphysical...
'Standalone' in my view refers to the application as a package, something that gets installed for a 'purpose', and in this sense Tersus is not 'packaged' as an application. If we were able to 'generate' an app from Tersus, ie: A self contained package (whether it includes a minimal Eclipse/Server configuration) that can either have its own installer (if necessary) or easily wrapped up in one.
Window decorations, like the Themes in Firefox, add to the 'theme' of the application. If these could be created with the Tersus Theme manager...
'Native' per se, not really fussed. If we can add images and use those as buttons/whatever, no problem.
I don't know if you recall Kai's Photo Soap (and other apps): They weren't native, they were cooler!
For best results, use the Firefox browser..